Details

sample56.0ms

Algorithm

intervals

Results

14.0ms	42×	body	2560	valid
9.0ms	193×	body	80	valid
4.0ms	99×	body	80	nan
4.0ms	16×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

67.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
48.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune202.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3.0 a) c))
4.4b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.4b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

7.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
56.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 3.0 a) c))
151.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
180.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	635	2579
1	3125	2333
2	5001	2320

prune394.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

localize23.0ms

Local error

Found 4 expressions with local error:

7.8b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
8.9b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
20.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))
20.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
4×	`pow1` `cbrt-div` `flip3--` `flip--`
3×	`associate-/r` `associate-/l`
2×	`pow1/3` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 71

Calls

4 calls:

15.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
32.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
6.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series928.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
638.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
98.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
100.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify93.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	632	1757
1	3022	1588
2	5003	1580

prune380.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3.0 a) c))
4.4b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
9.3b	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
20.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/r*`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
45.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
43.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 3.0 a) c))
148.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
184.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
77.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	682	1937
1	4416	1476
2	5002	1435

prune443.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.0b

regimes315.0ms

Accuracy

82.4% (4.7b remaining)

Error of 10.1b against oracle of 5.4b and baseline of 32.3b

bsearch116.0ms

Steps

Iters	Range		Point
9	5.4891008405958204e-108	7.205480219419598e-99	7.0970442891131365e-99
9	-7.026368034911783e+136	-2.129183190182848e+131	-5.5713700198328724e+135

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.3s

Algorithm

intervals

Results

244.0ms	1025×	body	2560	valid
232.0ms	5908×	body	80	valid
156.0ms	844×	body	1280	valid
110.0ms	2941×	body	80	nan
66.0ms	456×	body	640	valid
34.0ms	119×	body	5120	valid
25.0ms	228×	body	320	valid
7.0ms	101×	body	160	valid